Capital recovery factor

A capital recovery factor is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time. Using an interest rate i, the capital recovery factor is:

${\displaystyle CRF={\frac {i(1+i)^{n}}{(1+i)^{n}-1}}}$

where ${\displaystyle n}$ is the number of annuities received.^[1]

This is related to the annuity formula, which gives the present value in terms of the annuity, the interest rate, and the number of annuities.

If ${\displaystyle n=1}$, the ${\displaystyle CRF}$ reduces to ${\displaystyle 1+i}$. Also, as ${\displaystyle n\to \infty }$, the ${\displaystyle CRF\to i}$.

ExampleEdit

With an interest rate of i = 10%, and n = 10 years, the CRF = 0.163. This means that a loan of $1,000 $ at 10% interest will be paid back with 10 annual payments of $163.^[2]

Another reading that can be obtained is that the net present value of 10 annual payments of $163 at 10% discount rate is $1,000. 

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.